Physically-assisted Learning-based Quantitative Electromagnetic Inversion

Due to its strong penetration and non-interference by light,electromagnetic inverse scattering imaging has been widely used in various fields,such as satellite remote sensing,mine detection and so on.However,solving inverse scattering problems(ISPs)will encounter two major challenges:nonlinearity and ill-posedness.Especially in the case of the strong scatterers with high contrast and/or electrically large size,the nonlinearity is significantly improved.The main content of this thesis is to improve the inversion efficiency and accuracy of inverse scattering problems and make inverse scattering imaging applicable to a wider range of fields.Firstly,a classification network based inverse scattering imaging method is proposed in this thesis.In practice,the permittivity range of the unknown scatterer is unknown to us,so the dataset for training the neural network needs to cover a large range so that the inversion method can be applied to more scatterers.Therefore,the unknown scatterers can be classified according to the permittivity by a classification network.The approximate permittivity range of scatterers can be obtained by inputting the results of the back propagation(BP)algorithm into the classification network.Therefore,the subsequent inversion algorithm can obtain more physical prior information and reduce the complex of inversion.The numerical results show that the inversion accuracy is greatly improved after the classification network is used.In addition,we find that the proposed method can works well even when classification errors occur in the classification network.Secondly,the traditional nonlinear iterative inversion methods converge slowly,and easy to fall into local solution when dealing with the highly nonlinear ISPs.To alleviate the above challenges,this thesis proposes a learning-assisted inversion method(LAIM)which combines generative adversarial networks(GAN)and Fourier bases expansion with contraction integral equation for inversion(FBE-CIE-I).Firstly,the rough scatterer image with low-frequency component is recovered by FBE-CIE-I with less computational time.In the second step,the rough scatterer image is enhanced by GAN network.In GAN network,a self-attention layer is added at the end of the network to improve the inversion accuracy.In addition,we design a weighted loss function which combining adversarial loss,average absolute percentage error(MAPE)and structural similarity(SSIM)error.Both synthetic and experimental examples have validated the merits of the proposed LAIM.Finally,an unrolling algorithm of iterative contraction integral equation for subspace-based optimization method(CIE-SOM),named CIE-SOM-NET,is proposed for solving limited-aperture ISPs.The unrolling network which is composed of several sub-modules is designed to simulate the iteration process of CIE-SOM.In each module,CNN network is used to update the contrast source function,and least square method is used to update the modified contrast function.In addition,a weighted loss function,which is composed of the consistency function of the induced current,the scattered field,and the relative permittivity,is defined to constrain the training process of the network model.